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# Scaling Bitcoin workshop : Montreal 2015

### How to mine bitcoin profitably

How to mine bitcoin profitability

Minting money with megawatts

Thank you for the introduction. We thought bitcoin was really a good idea for an unstable and inefficient financial world. I am going to dive and talk about this presentation which is how to mine bitcoin profitably. This is a short talk, it's supposed to be a short talk, so let's get straight to the crux of the matter.

Bitcoin mining is the lowest part of the transaction stack. It scales. It's parallelizable. There might be second-order effects. Technology is clever. Technology is fun. Money makes the world go round. Economics imposes a constraint on us all. We wanted to ask the question, how much capacity could we profitably add to the network? And at what cost? This question really defines the economic scalability of bitcoin mining, and not the technologic scalability.

So we decided to construct a bitcoin mining profit function that would capture all of the first-order effects of bitcoin mining revenue and bitcoin mining cost. So let me walk you briefly through this equation. The profit function, you use pi to denote profit. pi(x) is additional capacity adding to the network is revenue minus operating costs minus capital costs. As you we all know, if we add capacity x it would capture a proportion of the bitcoin network and therefore a proportion of the bitcoin revenue, the supply is predetermined, we all know how that behaves. The bitcoin price is volatile and so are transaction fees. If we subtract the operating costs, then the first simplistic version of this used a variable c to note the op-ex costs. For the fixed costs, they are amortized over a period t and they scale, there's a variable, fixed costs of non-recurring engineering costs, and storage capacity. You can apply this to the system or the deployment environment. If you plot this equation, the revenues look like this, the investment cost look like this, and the operating cost look like this, you add the two and you get total cost, then between the two curves is your profit. If you have an area between these two curves, you can mine profitably. You can achieve break-even once you get fixed cost-- there is a point of maximum profitability, once your revenues start flattening off and you get the top curve intersection again, and there's a maximum capacity where you can still mine profitably, and then there's a point where the operation cost exceeds your revenue.

We can analytically solve for all of these points. The profit function determines network size. Let's look at maximum hashrate, it's inversely proportional to the...... Then you get some pretty large expression for the upper and lower break even costs. For the break even costs what you can do is if you set these equations, this determinant here, of this, under the square root here, you can find the roots of this equation and find what's the shortest payback period for you to recover your mining lesson.

We ran this on some data. We ran this on 3 generations of ASICs deployed on the network. We broke down the constant ... power efficiency of data center, measures the uptime of your system. [....]. Given these numbers, which are estimates, you can see that the first generation is no longer profitable. This is the growth in the hashrate of the network and it has exceeded the maximum hashrate of generation 1, it's close to exceeding the maximum hashrate of generation 2, but it still has a ways to go before it puts generation 3 out of business. These are the implied payback times, for generation 1 it's off the charts, generation 2 is heading off the charts in 1 year, and generation 3 maybe 10 years. For adding capacity to the system, let's say our amortization time is 3 years, that's not unreasonable because the maximum power efficiency doubles every 3 years. Then we can plot an actual function like this, these are the profits, and those are the revenues, those are the total costs for op-ex, and we see that for t equals 3, there's a network running at 368 petahash, the lower break even point is 373 petahash we can hit break-even once we add 5 petahashes of capacity. The other break-even point is 1300 petahashes, our sweet spot is about 700 petahash and we would be mining at 93% margin if we had this system deployed at the moment. The price of getting 5 petahash on to the network is approximately $10 million at the moment.

This is how the game will be played over the future. People will race to find cheap and free sources of energy. People will try to deploy cheap and efficient ASICs. I think that mining is far from equilibrium. Pursuing the existing technology in the .. scenario is that we can get up to 1300 petahash easily. I think at least one company in the space has announced plans for distributing processors in various places, and creating them at scale so that they are cheapl, and then embedding them into systems where whoever owns them.

Mining has room for profitable growth.